Finite Group DatabasebetaFinite Group DatabasebetaOrder 7552.
228 conjugacy classes of subgroups; only the 84 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 84 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C59 | #121 |
| commutator, Frattini, cosocle | C22×C4 | C23×C59 |
| prime radical | C22×D4×C59 | C22 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C59 ◁ C22×C4×C59 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#108×C59 | C2 | semidirect |
| 2. C59×#428 | C2 | semidirect |
| 3. C59×#424 | C2 | semidirect |
| 7. C59×#343 | C2 | semidirect |
| 91. #2063 | C59 | direct (N × H) |
| 98. C2×#108 | C2×C59 | semidirect |
| 99. #428 | C2×C59 | semidirect |
| 100. #424 | C2×C59 | semidirect |
| 104. #343 | C2×C59 | semidirect |
| 105. C59 | #2063 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#108×C59 | 2 |
| C59×#428 | 2 |
| C59×#424 | 2 |
| C59×#418 | 2 |
| C2×#102×C59 | 2 |
| C2×#100×C59 | 2 |
| C59×#343 | 2 |
| #2063 | 59 |